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Mirrors > Home > ILE Home > Th. List > breq12 | Unicode version |
Description: Equality theorem for a binary relation. (Contributed by NM, 8-Feb-1996.) |
Ref | Expression |
---|---|
breq12 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1 4005 |
. 2
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2 | breq2 4006 |
. 2
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3 | 1, 2 | sylan9bb 462 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-sn 3598 df-pr 3599 df-op 3601 df-br 4003 |
This theorem is referenced by: breq12i 4011 breq12d 4015 breqan12d 4018 posng 4697 isopolem 5820 poxp 6230 rbropapd 6240 ecopover 6630 ecopoverg 6633 ltdcnq 7393 recexpr 7634 ltresr 7835 reapval 8529 ltxr 9771 xrltnr 9775 xrltnsym 9789 xrlttr 9791 xrltso 9792 xrlttri3 9793 xposdif 9878 exmidsbthrlem 14630 |
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